Optimization with Sparsity-Inducing Penalties - Archive ouverte HAL Access content directly
Journal Articles Foundations and Trends in Machine Learning Year : 2011

Optimization with Sparsity-Inducing Penalties

Abstract

Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. They were first dedicated to linear variable selection but numerous extensions have now emerged such as structured sparsity or kernel selection. It turns out that many of the related estimation problems can be cast as convex optimization problems by regularizing the empirical risk with appropriate non-smooth norms. The goal of this paper is to present from a general perspective optimization tools and techniques dedicated to such sparsity-inducing penalties. We cover proximal methods, block-coordinate descent, reweighted $\ell_2$-penalized techniques, working-set and homotopy methods, as well as non-convex formulations and extensions, and provide an extensive set of experiments to compare various algorithms from a computational point of view.
Fichier principal
Vignette du fichier
Bach-Jenatton-Mairal-Obozinski-HAL.pdf (1.09 Mo) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-00613125 , version 1 (02-08-2011)
hal-00613125 , version 2 (20-11-2011)

Identifiers

Cite

Francis Bach, Rodolphe Jenatton, Julien Mairal, Guillaume Obozinski. Optimization with Sparsity-Inducing Penalties. Foundations and Trends in Machine Learning, 2011, ⟨10.1561/2200000015⟩. ⟨hal-00613125v2⟩
4023 View
3240 Download

Altmetric

Share

Gmail Facebook X LinkedIn More